Expert Tips for Tutoring Algebra: Avoiding Common Mistakes

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The discussion centers on helping college algebra students who struggle with the concept of manipulating equations, particularly the misconception of "moving" terms from one side to another. This misunderstanding leads to frequent sign errors and complications with radicals. It is suggested that a solid grasp of fundamental properties of real numbers, equality, and operations is essential for these students. Reteaching concepts such as the commutative and associative properties, distribution, and the laws of exponents is recommended. Emphasizing the importance of performing the same operation on both sides of the equation, rather than "moving" terms, can clarify the process. Using examples to illustrate this method, such as isolating a variable through inverse operations, can reinforce understanding and reduce mistakes. Overall, a focus on foundational skills and clear examples is key to improving their algebraic proficiency.
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Im not a math master yet. I'm a physics major in calc. 3 at the moment and I am trying to help a couple friends in college algebra. They both have this conceptual problem of thinking they are "moving" stuff from one side of the equation. It is causing tons of sign mistakes and causing a lot of trouble with radicals and such.
Does anyone have some good examples that show your just doing the same thing to both sides of the equation, or is the best way to do a lot of examples and make the "show all their work'?
Thanks!
 
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Your friends in College Algebra studied and should have mastered some important properties of Real Numbers and properties of equality and of inequality part-way into their study of Intermediate Algebra; even possibly before they finished Introductory Algebra. Spend time reteaching your friends the commutative and associative properties for addition and multiplication, the distribution property, the identity properties, and the ...can not remember what you call them... properties of equality and inequality. Also substitution principle. They need to know the properties and to have acquired the associated skills, so maybe you can just reteach them to your friends. You might also give a review of laws of exponents. Pick any book you like to use for teaching (reteaching) these ideas and skills.

Really, if these College Algebra students are having the trouble as you have described, the earned prerequisites for the course are dubious. (Maybe "dubious" is the wrong choice of word.)
 
Of course you are really doing the same thing to both sides. But a short cut is to cancel the operation and do the opposite operation to the other side. This always gives you the right sign and takes less thought and time.
 
harvellt said:
Im not a math master yet. I'm a physics major in calc. 3 at the moment and I am trying to help a couple friends in college algebra. They both have this conceptual problem of thinking they are "moving" stuff from one side of the equation. It is causing tons of sign mistakes and causing a lot of trouble with radicals and such.
Does anyone have some good examples that show your just doing the same thing to both sides of the equation, or is the best way to do a lot of examples and make the "show all their work'?
Thanks!

If that's the case then don't "move" stuff from one side to the other.

Do the inverse operation to BOTH sides.

say x+2=4
x+2-2=4-2 because you are trying to ISOLATE x by itself
which leaves you with x=2
 

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